Triangular-pyramidal cube-corner retroreflection sheet

ABSTRACT

A triangular-pyramidal cube-corner retroreflective sheeting characterized in that a lateral face (prism face) (face c) using a base edge (x) of triangular-pyramidal reflective elements faced each other and arranged in the closest-packed state by sharing the base edge (x) on a base plane (X-X′) as one side is hexagonal or triangular, two other faces (faces a and b) sharing one ridge line starting with an apex (H) of the triangular-pyramidal reflective elements is quadrangular and when assuming the height from the apex (H) up to the base plane (X-X′) as (h) and the height up to a substantially horizontal plane (Z-Z′) including base edges (z and w) of other two faces (faces a and b) as (h 0 ), and the angle formed between the optical axis of the triangular-pyramidal reflective elements and a plane (Y-Y′) including the base edge (x) and vertical to the base plane (X-X′) as (θ), h and h 0  are not substantially equal to each other but h/h 0  and θ meet a specific relational expression.

TECHNICAL FIELD

The present invention relates to a triangular-pyramidal cube-cornerretroreflective sheeting having a novel structure. More minutely, thepresent invention relates to a triangular-pyramidal cube-cornerretroreflective sheeting in which triangular-pyramidal reflectiveelements having a novel structure are arranged in the closest-packedstate.

Still more minutely, the present invention relates to a cube-cornerretroreflective sheeting constitute of triangular-pyramidal cube-cornerretroreflective elements (hereafter referred to as triangular-pyramidalreflective elements or merely, elements) useful for signs includingtraffic signs and construction work signs, license plates of automobilesand motorcycles, safety materials of clothing and life preservers,markings of signboards, and reflectors of visible-light, laser-beam, andinfrared-ray reflective sensors.

Still further minutely, the present invention relates to atriangular-pyramidal cube-corner retroreflective sheeting characterizedin that triangular-pyramidal cube-corner retroreflective elementsprotruded beyond a common base plane (X-X′) are faced each other andarranged on the base plane (X-X′) in the closest-packed state by sharingone base edge on the base plane (X-X′), the base plane (X-X′) is acommon plane including many base edges (x, x, . . . ) shared by thetriangular-pyramidal reflective elements, the two triangular-pyramidalreflective elements faced each other constitute an element pair havingsubstantially same shape faced so as to be respectively substantiallysymmetric to planes (Y-Y′, Y-Y′, . . . ) vertical to the base plane(X-X′) including many shared base edges (x, x, . . . ) on the base plane(X-X′), the triangular-pyramidal reflective elements are constituted ofsubstantially same hexagonal or triangular lateral faces (prism faces)(faces c₁ and c₂) using the shared base edges (x, x, . . . ) as onesides and substantially same quadrangular lateral faces (faces a₁ and b₁and faces a₂ and b₂) substantially orthogonal to the face c₁ or the facec₂ by using two upper sides of the face c₁ or c₂ starting with apexes(H₁ and H₂) of the triangular-pyramidal reflective elements as one sidesand sharing one ridge line of the triangular-pyramidal reflectiveelements and using the ridge line as one side, and when assuming theheight from the apexes (H₁ and H₂) of the triangular-pyramidalreflective elements up to the base plane (X-X′) including the base edges(x, x, . . . ) of the hexagonal or triangular lateral faces (faces c₁and c₂) of the triangular-pyramidal reflective elements as (h), theheight from the apexes (H₁ and H₂) of the triangular-pyramidalreflective elements up to a substantially horizontal plane (Z-Z′)including base edges (z and w) of other lateral faces (faces a₁ and b₁and faces a₂ and b₂) of the triangular-pyramidal reflective elements as(h₀), the intersection between a vertical line from the apexes (H₁ andH₂) of the triangular-pyramidal reflective elements to the base plane(X-X′) and the base plane (X-X′) as P, the intersection between anoptical axis passing through the apexes (H₁ and H₂) and the base plane(X-X′) as Q, and moreover, expressing distances from the intersections(P) and (Q) up to planes (Y-Y′, Y-Y′, . . . ) including the base edges(x, x, . . . ) shared by the triangular-pyramidal reflective elementsand vertical to the base plane (X-X′) as p and q, and assuming the angleformed between the optical axis and the vertical plane (Y-Y′) as (θ),the above h and h₀ are not substantially equal and meet the followingexpression (1).

$\begin{matrix}{{0.5R}\quad \leqq \quad \frac{h}{h_{0}} \leqq \quad {1.5R}} & (1)\end{matrix}$

(In the above expression, R is defined by the following expression.)$R = \frac{{\sin \left( {35.2644^{*} - \theta} \right)} + {1.2247\quad \sin \quad \theta}}{\sin \left( {35.2644^{*} - \theta} \right)}$

(In the above expression, it is assumed that when the value of the above(p−q) is negative, θ takes a negative (−) value.)

BACKGROUND ART

A retroreflective sheeting for reflecting incoming light toward a lightsource has been well known so far and the sheeting using itsretroreflective characteristic is widely used in the above fields.Particularly, a retroreflective sheeting using the retroreflectiveprinciple (theory) of a cube-corner retroreflective element such as atriangular-pyramidal reflective element is extremely superior to aconventional retroreflective sheeting using micro glass beads inretroreflectivity and its purpose has been expanded year by year becauseof its superior retroreflective performance.

However, though a conventionally-publicly-known triangular-pyramidalretroreflective element shows a preferable retroreflectivity when theangle formed between the optical axis of the element {axis passingthrough the apex of the triangular pyramid of the triangular-pyramidalretroreflective element equally separate from three lateral faces (facesa, b, and c)} constituting a triangular-pyramidal cube-cornerretroreflective element and intersecting each other at an angle of 90°and an incident light (the angle is hereafter referred to as entranceangle) is kept in a small range, the retro-reflectivity rapidlydeteriorates as the entrance angle increases (that is, the entranceangularity deteriorates).

Moreover, the reflection principle (theory) of a triangular-pyramidalretroreflective element uses internal total reflection caused on theinterface between air and a transparent medium constituting thetriangular-pyramidal reflective element when light is emitted to airfrom the transparent medium at a specific angle {critical angle (α_(c))}or more. The critical angle (α_(c)) is shown as the following expressionby a refractive index (n) of a transparent medium constituting atriangular-pyramidal reflective element and a refractive index (n₀) ofair.

${\sin \quad \alpha_{c}} = \frac{n_{0}}{n}$

In this case, it is allowed to consider the refractive index (n₀) of airis almost equal to 1 and constant. Therefore, the critical angle (α_(c))decreases as the value of the refractive index (n) of the transparentmedium increases and light easily reflects from the interface betweenthe transparent medium and air. When using a synthetic resin for atransparent medium, the critical angle (α_(c)) shows a comparativelylarge value of approx. 42° because most synthetic resins have arefractive index of approx. 1.5.

Light incoming to the surface of a retroreflective sheeting using theabove triangular-pyramidal reflective element at a large entrance anglereaches the interface between the triangular-pyramidal reflectiveelement and air at a comparatively small angle from a lateral face(reflecting surface) of the reflective element after passing through thetriangular-pyramidal reflective element. When the comparatively smallangle is smaller than the critical angle (α_(c)), the light passesthrough the back of the element without totally reflecting from theinterface. Therefore, a retroreflective sheeting using atriangular-pyramidal reflective element has a disadvantage that it isgenerally inferior in entrance angularity.

However, because a triangular-pyramidal retroreflective element is ableto reflect light in the light incoming direction over almost entiresurface of the element, reflected light does not reflect by emanating toa wide angle due to spherical aberration like a micro-glass-beadreflective element. However, in practical use, the narrow divergenceangle of retroreflected light easily causes a trouble that the lightemitted from a head lamp of an automobile does not easily reach eyes ofa driver present at a position separate from the optical axis of thelight such as eyes of the driver when the light is retroreflected from atraffic sign. The above trouble more frequently occurs particularly whenan automobile approaches a traffic sign because the angle (observationangle) formed between a light entrance axis and an axis connecting adriver and a reflection point (that is, the observation angularitydeteriorates).

Many proposals have been made so far for the above cube-cornerretroreflective sheeting, particularly for a triangular-pyramidalcube-corner retroreflective sheeting and various improvements andstudies are made.

For example, Jungersen's U.S. Pat. No. 2,481,757 discloses aretroreflective sheeting constituted by arranging retroreflectiveelements of various shapes on a thin sheeting and a method formanufacturing the sheeting. Triangular-pyramidal reflective elementsdisclosed in the above U.S. patent include a triangular-pyramidalreflective element in which the apex is located at the center of abase-plane triangle and the optical axis does not tilt and atriangular-pyramidal reflective element in which the apex is not locatedat the center of a base-plane triangle but the optical axis tilts.More-over, it is described in the U.S. patent to efficiently reflectlight toward an approaching automobile. Furthermore, it is describedthat the size of a triangular-pyramidal reflective element, that is, thedepth of the element is {fraction (1/10)}″ in (2,540 μm) or less.Furthermore, FIG. 15 in the U.S. patent illustrates atriangular-pyramidal reflective element whose optical axis tilts in theplus (+) direction similarly to the case of a preferred mode of thepresent invention. The tilt angle (θ) of the optical axis is estimatedas approx. 6.5° when obtaining it from the ratio between the longer edgeand shorter edge of the base-triangular plane of the illustratedtriangular-pyramidal reflective element.

However, the above Jungersen's U.S. patent does not specificallydisclose a very small triangular-pyramidal reflective element shown inthe present invention or it does not disclose a size or an optical-axistilt which a triangular-pyramidal reflective element must have in orderto show superior observation angularity and entrance angularity.

Moreover, Stamm's U.S. Pat. No. 3,712,706 discloses a retroreflectivesheeting in which the so-called equilateral triangular-pyramidalcube-corner retroreflective elements in which shapes of their base-planetriangles are equilateral triangular and shapes of three other sides areright isosceles triangular are arranged on a thin sheeting so that theirbase planes are brought into the closest-packed state on a common plane.Stamm's U.S. patent solves the problem that retroreflectivity isdeteriorated due to increase of an entrance angle through mirrorreflection by vacuum-coating the reflective surface of a reflectiveelement with a metal such as aluminum and the above trouble that thelight incoming at an angle of less than an internal total-reflectioncondition passes through the interface between elements and thereby, itdoes not retroreflect.

However, because the above Stamm's proposal uses the mirror reflectionprinciple (theory) as means for improving the angularity (wideangularity), the proposal easily causes the trouble that the appearanceof an obtained retroreflective sheeting becomes dark or the reflectivebrightness easily deteriorates because a metal such as aluminum orsilver used for the mirror surface is oxidized due to incoming water orair while it is used. Moreover, the proposal does not describe means forimproving the angularity (wide angularity) by a tilt of an optical axisat all.

Moreover, Hoopman's European Pat No. 137,736(B) discloses aretroreflective sheeting in which triangular-pyramidal cube-cornerretroreflective elements with a tilted optical axis whose triangularbase-plane is isosceles triangular are brought into the closest-packedstate on a common plane. Moreover, it is described that the optical axisof a triangular-pyramidal cube-corner retroreflective element disclosedin the patent tilts in a negative (−) direction and its tilt angleapproximately ranges between 7° and 13°.

However, according to the relation between reflective brightness andoptical-axis tilt examined by the present inventor et al. through thelight tracing method, it is found that reflective brightness lowers asthe tilt angle of a optical axis exceeds 4° and further increases in anegative direction and particularly, the reflective brightness of atriangular-pyramidal reflective element whose optical axis exceeds 6° ina negative direction extremely lowers. This may be because areas ofthree prism faces a, b, and c forming a triangular-pyramidal reflectiveelement whose optical axis does not tilt are equal to each other butareas of faces a and b of an element whose optical axis tilts in anegative direction slowly decrease compared to the area of the face c ofthe element as the tilt angle of the element increases.

Moreover, Szczech's U.S. Pat. No. 5,138,488 also discloses aretroreflective sheeting in which titled triangular-pyramidalcube-corner retroreflective elements whose base planes are isoscelestriangular are arranged on a thin sheeting so that the base planes arebrought into the closest-packed state. In the U.S. patent, optical axesof the triangular-pyramidal reflective elements tilt in the direction ofa side shared by paired triangular-pyramidal reflective elements facedeach other and it is specified that the tilt angle approximately rangesbetween 2° and 5° and the size of an element ranges between 25 and 100μm.

Furthermore, European Pat. No. 548,280(B1) corresponding to the aboveU.S. patent discloses that the distance between a plane including acommon side of paired triangular-pyramidal cube-corner retroreflectiveelements and vertical to a common plane and the apex of the element isnot equal to the distance between the intersection with the common planeof the optical axis of the element and the vertical plane, that is, thetilt of the optical axis may be either of positive (+) and negative (−)directions, and its tilt angle approximately ranges between 2° and 5°,and the size of the element ranges between 25 and 100 μm.

As described above, in the case of Szczech's European Pat. No.548,280(B1), the tilt of an optical axis approximately ranges between 2°and 5° including positive (+) and negative (−) directions. However, inthe case of the tilt of the optical axis in the range of the Szczech'sinvention, wide angularity, particularly entrance angularity is notadequately improved.

The conventionally-publicly-known triangular-pyramidal cube-cornerretroreflective elements of Jungersen's U.S. Pat. No. 2,481,757, Stamm'sU.S. Pat. No. 3,712,706, Hoopman's European Pat. No. 137,736(B1),Szczech's U.S. Pat. No. 5,138488 and European Pat. No. 548,280(B1) arecommon to each other in that base planes of many triangular-pyramidalreflective elements serving as a core of entrance and reflection oflight are present on the same plane. Thus, every retroreflectivesheeting constituted of triangular-pyramidal reflective elements whosebase planes are present on the same plane is inferior in entranceangularity, that is, it has a disadvantage that retroreflectivebrightness suddenly deteriorates when an entrance angle of light to thetriangular-pyramidal reflective element increases.

DISCLOSURE OF THE INVENTION

In general, not only high brightness, that is, level (magnitude) ofreflective brightness of the light incoming from the front of atriangular-pyramidal cube-corner retroreflective sheeting but also wideangularity of the light are requested as basic optical characteristicsof the sheeting and moreover, three performances such as observationangularity, entrance angularity, and rotational angularity are requestedfor the wide angularity.

As described above, every conventionally-publicly-known retroreflectivesheeting constituted of triangular-pyramidal cube-corner retroreflectiveelements has been inferior in entrance angularity and observationangularity. However, the present inventor et al. found throughlight-tracing simulation that it is possible to improve the entranceangularity of a retroreflective sheeting constituted oftriangular-pyramidal reflective elements by making the height (h′) fromthe plane (X-X′) including many base edges (x, x, . . . ) shared by thetriangular-pyramidal reflective elements set at symmetric positions eachother up to the apexes (H₁ and H₂) of the elements substantially largerthan the height (h) from the plane (Z-Z′) including base edges (z and w)of two faces (faces a and b) substantially orthogonal to the face chaving one base edge shared by the triangular-pyramidal reflectiveelements as one side up to the apex of the reflective elements andapplied a patent. (Japanese Patent Application No. 295907/1996).

Moreover, the present inventor et al. continued the study by lighttracing simulation and found that it is also possible to improve theentrance angularity of a retroreflective sheeting constituted of twotriangular-pyramidal reflective elements faced each other by making theheight (h′) from the first plane (X-X′) including base edges (x, x, . .. ) of lateral faces (faces c₁ and c₂) having base edges (x, x, . . . )shared by the triangular-pyramidal reflective elements as one side up tothe apexes (H₁ and H₂) of the triangular-pyramidal reflective elementssubstantially smaller than the height (h) from thesubstantially-horizontal second base plane (Z-Z′) including the baseedges (z and w) of other lateral faces (faces a₁ and b₁ and faces a₂ andb₂) of the triangular-pyramidal reflective elements up to the apexes (H₁and H₂) of the triangular-pyramidal reflective elements and applied apatent.

(Japanese Patent Application No. 330836/1997)

The present inventor et al. further continued the study that theimprovement in the above two applied patents was achieved by minimizingthe problem of relatively enlarging or contracting sizes of the lateralfaces (faces c₁ and c₂) which had been conventionally caused by a tiltof an optical axis compared to other lateral faces (faces a₁ and b₁ andfaces a₂ and b₂). As a result, we found that the ratio between theheight (h) from the base plane (X-X′) including common base edges (x, x. . . ) of the lateral faces c₁ and c₂ faced with thetriangular-pyramidal reflective element pair up to the apexes (H₁ andH₂) of the element pair and the height (h₀) from one horizontal plane(Z-Z′) including the base edges (z and w) of the twosubstantially-same-shaped lateral faces (faces a₁ and b₁ and faces a₂and b₂) of the element pair up to the apexes (H₁ and H₂) of the elementpair must be kept in a specific range shown by a tilt angle θ of anoptical axis and a specific relational expression and finished thepresent invention.

Therefore, the present invention relates to a triangular-pyramidalcube-corner retroreflective sheeting characterized in thattriangular-pyramidal cube-corner retroreflective elements protrudedbeyond a common base plane (X-X′) are faced each other and arranged inthe closest-packed state by sharing one base edge on the base plane(X-X′), the base plane (X-X′) is a common plane including many baseedges (x, x, . . . ) shared by the triangular-pyramidal reflectiveelements, the two triangular-pyramidal reflective elements faced eachother constitute an element pair having substantially same shape facedso as to be respectively substantially symmetric to planes (Y-Y′, Y-Y′,. . . ) vertical to the base plane (X-X′) including many shared baseedges (x, x, . . . ) on the base plane (X-X′), the triangular-pyramidalreflective elements are constituted of substantially same hexagonal ortriangular lateral faces (faces c₁ and c₂) using the shared base edges(x, x, . . . ) as one sides and substantially same quadrangular lateralfaces (faces a₁ and b₂ and faces a₂ and b₂) substantially orthogonal tothe face c₁ or the face c₂ by using upper two sides of the face c₁ orface c₂ starting with apexes (H₁ and H₂) of the triangular-pyramidalreflective elements as one sides and sharing one ridge line of thetriangular-pyramidal reflective elements and using the ridge line as oneside, and when assuming the height from the apexes (H₁ and H₂) of thetriangular-pyramidal reflective elements up to the base plane (X-X′)including the base edges (x, x, . . . ) of the hexagonal or triangularlateral faces (face c₁ and face c₂) of the triangular-pyramidalreflective elements as (h), the height from the apexes (H₁ and H₂) ofthe triangular-pyramidal reflective elements up to a substantiallyhorizontal plane (Z-Z′) including base edges (z and w) of other lateralfaces (faces a₁ and b₂ and faces a₂ and b₂) of the triangular-pyramidalreflective elements as (h₀), the intersection between a vertical linefrom the apexes (H₁ and H₂) of the triangular-pyramidal reflectiveelements to the base plane (X-X′) and the base plane (X-X′) as P, theintersection between an optical axis passing through the apexes (H₁ andH₂) and the base plane X-X′) as Q, and moreover, expressing distancesfrom the intersections (P) and (Q) up to planes (Y-Y′, Y-Y′, . . . )including the base edges (x, x, . . . ) shared by thetriangular-pyramidal reflective elements and vertical to the base plane(X-X′) as p and q, and assuming the angle formed between the opticalaxis and the vertical plane (Y-Y′) as (θ), the above h and h₀ are notsubstantially equal and meet the following expression (1).$\begin{matrix}{{0.5\quad R} \leqq \frac{h}{h_{0}} \leqq {1.5\quad R}} & (1)\end{matrix}$

(In the above expression, R is defined by the following expression.)$R = \frac{{\sin \left( {35.2644^{*} - \theta} \right)} + {1.2247\sin \quad \theta}}{\sin \left( {35.2644^{*} - \theta} \right)}$

(In the above expression, it is assumed that when the value of the above(p−q) is negative, θ takes a negative (−) value.)

The present invention is more minutely described below by properlyreferring to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a top view of a positively-tilted triangular-pyramidalcube-corner retroreflective element group according to the prior art;

FIG. 2 is a sectional view of the positively-tilted triangular-pyramidalcube-corner retroreflective element group shown in FIG. 1 according tothe prior art, when cut by the sectional line (L-L′);

FIG. 3 is a top view of a negatively-tilted triangular-pyramidalcube-corner retroreflective element group according to the prior art;

FIG. 4 is a sectional view of the negatively-tilted triangular-pyramidalcube-corner retroreflective element group shown in FIG. 2 according tothe prior art, when cut by the sectional line (L-L′);

FIG. 5 is a top view of a positively-tilted triangular-pyramidalcube-corner retroreflective element group for explaining the presentinvention;

FIG. 6 is a sectional view of the positively-tilted triangular-pyramidalcorner retroreflective element group shown in FIG. 5 for explaining thepresent invention, when cut by the sectional line (L-L′) in FIG. 5;

FIG. 7 is an enlarged top view of a pair of positively-tiltedtriangular-pyramidal reflective elements for explaining the presentinvention;

FIG. 8 is a side view of the positively-tilted triangular-pyramidalreflective element pair shown in FIG. 7 for explaining the presentinvention, when viewed from the line (L-L′ in FIG. 7;

FIG. 9 is a top view of a negatively-tilted triangular-pyramidalcube-corner retroreflective element group shown in FIG. 9 for explainingthe invention;

FIG. 10 is a sectional view of the negatively-tilted triangular-pyramidcube-corner retroreflective element group shown in FIG. 9 for explainingpresent invention, when cut by the sectional line (L-L′) in FIG. 9;

FIG. 11 is an enlarged top view of a pair of negatively-tiltedtriangular-pyramidal reflective elements for explaining the presentinvention;

FIG. 12 is a side view of the negatively-tilted triangular-pyramidalrejective element pair shown in FIG. 11 for explaining the presentinvention, when viewed from the line (L-L′) in FIG. 11; and

FIG. 13 is a sectional view showing a structure of a negatively-tiltedre/reflective sheeting that is one of modes of a triangular-pyramidalcube-corner retroreflective sheeting of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

Before explaining the present invention, a conventionally-publicly-knownart is first described below.

FIGS. 1 to 4 show top vies and sectional views for explaining atriangular-pyramidal cube-corner retroreflective element according tothe prior art for comparison with a triangular-pyramidal cube-cornerretroreflective element of the present invention.

In FIGS. 1 and 3, base edges of triangular-pyramidal cube-cornerretroreflective elements protruded beyond a common plane are arranged ona common plane (X-X′) in the closest-packed state as a pair oftriangular-pyramidal reflective elements sharing one base edge (x, x, .. . ) and faced each other so as to be substantially symmetric to aplane (Y-Y′) vertical to a base plane (X-X′) including the shared baseedge (x, x, . . . ).

Moreover, FIGS. 2 and 4 show sectional views of the triangular-pyramidalreflective elements cut by sectional lines (L-L′) of the element groupsshown in FIGS. 1 and 3. The element pairs of a tiltedtriangular-pyramidal cube-corner retroreflective sheeting have opticalaxes oriented in the opposite direction to each other. When assuming thedistance from the intersection (P) between a vertical line extended fromthe apex (H) of the element to the base plane (X-X′) and the base plane(X-X′) up to the base edges (x, x, . . . ) shared by the element pair as(p) and the distance from the intersection (Q) between an optical axisand the base plane up to the base edges (x, x, . . . ) shared by theelement pair as (q), the optical axis tilts from the vertical plane(Y-Y′) in a direction in which the difference (q−p) becomes positive (+)in FIG. 2 and negative (−) in FIG. 4. FIG. 5 and 6 show a top view and asectional view for explaining triangular-pyramidal cube-cornerretroreflective elements of the present invention.

In FIG. 5, it is shown that positively-tilted triangular-pyramidalcube-corner retroreflective elements having three lateral facessubstantially orthogonal to each other and protruded beyond a commonbase plane (X-X′) are faced each other and arranged on a substrate inthe closest-packed state by sharing one base edge (x, x, . . . ) on thebase plane (X-X′).

FIG. 6 shows a sectional view of a positively-tiltedtriangular-pyramidal reflective element of the present invention whencut by the sectional line (L-L′) of the element group shown in FIG. 5.As shown in FIG. 5, the positively-tilted triangular-pyramidalreflective element of the present invention is constituted of hexagonallateral faces (faces c₁ and c₂) faced each other by shaking one baseedge (x) on the base plane (X-X′) and substantially-same-shapedquadrangular lateral faces (faces a₁ and b₂ and faces a₂ and b₂)substantially orthogonal to the face c₁ or c₂ using upper two sides ofthe face c₁ or c₂ starting with apexes (H₁ and H₂) of thetriangular-pyramidal reflective elements as one sides, sharing one ridgeline of the triangular-pyramidal reflective element, and using the ridgeline as one side.

As shown in FIG. 5, positively-tilted triangular-pyramidal reflectiveelements each of which is one of modes of the present invention arearranged on a substrate in the closest-packed state at a repetitivepattern by sharing a base edge (x) on the base plane (X-X′) and forminga substantially-same-shaped element pair faced each other so as to besubstantially symmetric. Therefore, the common base edge (x) constitutesa continuous straight line. Moreover, many base edges (x) shared byother adjacent triangular-pyramidal reflective element groups areparallel with a straight line constituting the base edges (x) and formparallel straight-line groups having equal repetitive pitches.

Therefore, the lateral faces (c₁ and c₂ faces) of the positively-tiltedtriangular-pyramidal reflective element of the present invention arefaced each other by sharing a base edge (x) and the base edge (x)constitutes a continuous straight line. Therefore, the face c₁ forms acontinuous plane and the face c₂ also forms a continuous plane.Moreover, the quadrangular lateral faces (small quadran-gular lateralfaces surrounded by faces a₁ and b₂ and two c₂ faces) are also locatedon a plane on the line x formed by the face c₁ or c₂. As a result, thebase edge of the plane formed by the face c₁ or c₂ and the lateral facehaving the small quadrangle is present on the above continuous straightline and has a lateral face same as the face c whose cross section formsa V-shaped groove.

The term “substantial” in this description is an expression includingeven a very slight difference. For example, “substantially symmetric”and “substantially same shape” are expressions including a case in whichcorresponding side and/or angle is or are completely the same and themagnitude of the side or angle is very slightly different.

To easily understand the present invention, an enlarged top view of apair of positively-tilted triangular-pyramidal reflective elements shownas the following patterns in FIG. 5 is shown in FIG. 7 and a side viewfrom the arrow shown by the line L-L′ in FIG. 7 is shown in FIG. 8.

In FIGS. 7 and 8, the face c₁ of the right element R₁ (that is, theelement shown by the following pattern in FIG. 5) of a pair ofpositively-tilted triangular-pyramidal reflective element of the presentinvention is a hexagonal plane surrounded by points H₁-D₁-A-B-E₁, theface a₁ is a quadrangular plane surrounded by points H₁-J₁-G₁-E₁, thefaces a₁ and b₂ have substantially the same shape, and the faces c₁, a₁,and b₂ are substantially orthogonal to each other.

Moreover, the base plane of the right triangular-pyramidal reflectiveelement R₁ shown by a plane A-B-K₁ forms a part of a common base plane(X-X′).

In FIGS. 7 and 8, the left triangular-pyramidal reflective element shownby R₂ corresponds to the left triangular-pyramidal reflective element ofthe above pair of elements shown as the following pattern in FIG. 5 andthe left triangular-pyramidal reflective element R₂ whose base plane isshown by A-B-K₂ has the same shape as the right reflective element R₁whose base plane is shown by A-B-K₁ and the both elements are located atthe both sides of the base edge (A-B) (present on the common bas edge xin FIG. 5) shared by the both elements, and the left element R₂ has ashape obtained by rotating the right element R₁ by 180° counterclockwiseon the base plane (X-X′) about the middle point (O) of the base edge(A-B) shared by the both elements.

Therefore, in FIG. 7, the face c₂ shown by the points H₂-D₂-B-A-E₂ ofthe left element R₂ and the face a₂ shown by the points H₂-J₂-F₂-D₂, andthe face b₂ shown by the points H₂-J₂-G₂-E₂ have the same shape as thefaces c₁, a₁, and b₁ of the right element R₁ and the faces c₂, a₂, andb₂ are substantially orthogonal (90°) to each other.

Therefore, in FIG. 8 which is a side view from the line L-L′ directionin FIG. 7, the side view of the right element R₁ shown by the pointsB-H₁-J₁-K₁ and the side view of the left element R₂ shown by the pointsB-H₂-J₂-K₂ are substantially symmetric to right and left and have thesame shape.

As shown in FIG. 8, apexes of positively-tilted triangular-pyramidalreflective elements (R₁ and R₂) are shown by H₁ and H₂ and the heightfrom the base plane (X-X′) including the base edge x common to theapexes (H₁ and H₂) is shown by h.

As shown in FIGS. 7 and 8, the height h corresponds to the depth from aplane (virtual plane) including the apexes H₁ and H₂ of thepositively-tilted triangular-pyramidal reflective elements R₁ and R₂ ofthe present invention in the V-shaped valley formed by the faced facesc₁ and c₂ of the elements R₁ and R₂.

Moreover, as clearly shown in FIGS. 7 and 8, quadrangular lateral facesa₁ and b₁ and quadrangular lateral faces a₂ and b₂ of thepositively-tilted triangular-pyramidal reflective elements R₁ and R₂ ofthe present invention have substantially the same shape, base edgesF₁-D₁ and G₁-E₁ of the lateral faces a₁ and b₁ of the element R₁ andbase edges F₂-D₂ and G₂-E₂ of the lateral faces as and b₂ of the elementR₂ are present on the same horizontal plane (Z-Z′), and the height fromthe horizontal plane Z-Z′ up to a plane (virtual plane) including apexesH₁ and H₂ of the elements R₁ and R₂ is shown by h₀ in FIG. 8.

Therefore, the depth of a valley formed between the lateral faces a₁ andb₂ and lateral faces a₂ and b₂ of the positively-tiltedtriangular-pyramidal reflective elements R₁ and R₂ of the presentinvention and corresponding lateral faces of adjacent other elementsfrom a plane including the apexes H₁ and H₂ (the bottom of the valleycorresponds to base edges of the lateral faces a₁ and b₂ and lateralfaces a₂ and b₂) is shown by h₀.

In the case of a positively-tilted triangular-pyramidal reflectiveelement of the present invention, base edges of the faces a₁ and a₂ ofthe elements R₁ and R₂ are located on a common line z, base edges of thefaces b₂ and b₂ are located on a line w, and base edges of the faces c₁and c₂ are located on a common line x as shown in FIGS. 5 and 7.

Moreover, as shown in FIGS. 5 to 8 and previously described, a pluralityof positively-tilted triangular-pyramidal reflective elements of thepresent invention share the base edge (x, x, . . . ) shared by two cfaces to which the elements correspond and they are faced each other andarranged on a substrate in the closest-packed state.

A positively-tilted triangular-pyramidal cube-corner retroreflectivesheeting of the present invention is described below by referring toFIGS. 5 to 8. That is, triangular-pyramidal cube-corner retroreflectiveelements protruded beyond a common base plane (X-X′) are faced eachother and arranged in the closest-packed state by sharing one base edgeon the base plane (X-X′), the base plane (X-X′) is a common planeincluding many base edges (x, x . . . ) shared by thetriangular-pyramidal reflective elements, the two triangular-pyramidalreflective elements faced each other constitute an element pair havingsubstantially same shape faced so as to be respectively substantiallysymmetric to planes (Y-Y′, Y-Y′, . . . ) vertical to the base plane(X-X′) including many shared base edges (x, x . . . ) on the base plane(X-X′), the triangular-pyramidal reflective elements are constituted ofsubstantially same hexagonal lateral faces (faces c₁ and c₂) using theshared base edges (x, x, . . . ) as one sides and substantially samequadrangular lateral faces (faces a₁ and b₂ and faces a₂ and b₂)substantially orthogonal to the face c₁ or the face c₂ by using uppertwo sides of the face c₁ or c₂ starting with apexes (H₁ and H₂) of thetriangular-pyramidal reflective elements as one sides and sharing oneridge line of the triangular-pyramidal reflective elements and using theridge line as one side, and when assuming the height from the apexes (H₁and H₂) of the triangular-pyramidal reflective elements up to the baseplane (X-X′) including the base edges (x, x, . . . ) of the hexagonallateral faces (faces c₁ and c₂) of the triangular-pyramidal reflectiveelements as (h), the height from the apexes (H₁ and H₂) of thetriangular-pyramidal reflective elements up to a substantiallyhorizontal plane (Z-Z′) including base edges (z and w) of other lateralfaces (faces a₁ and b₁ and faces a₂ and b₂) of the triangular-pyramidalreflective elements as (h₀), the intersection between a vertical linefrom the apexes (H₁ and H₂) of the triangular-pyramidal reflectiveelements to the base plane X-X′) and the base plane (X-X′) as P, theintersection between an optical axis passing through the apexes (H₁ andH₂) and the base plane (X-X′) as Q, and moreover, expressing distancesfrom the intersections (P) and (Q) up to planes (Y-Y′, Y-Y′, . . . )including the base edges (x, x, . . . ) shared by thetriangular-pyramidal reflective elements and vertical to the base plane(X-X′) as p and q, the optical axis tilts in a direction in which (q−p)becomes positive (+) and the above h and h₀ are not substantially equalto each other.

FIGS. 9 and 10 show a top view and a sectional view for explainingnegatively-tilted triangular-pyramidal cube-corner retro-reflectiveelements of the present invention. FIG. 9 shows thattriangular-pyramidal cube-corner retroreflective elements protrudedbeyond a common base plane (X-X′) share a base edge (x) on the baseplane, and they are faced each other and arranged on the base plane inthe closest-packed state.

Moreover, FIG. 10 shows a sectional view of negatively-tiltedtriangular-pyramidal reflective elements of the present invention cut bythe sectional line (L-L′) of the element group shown in FIG. 9. As shownin FIG. 9, the negatively-tilted triangular-pyramidal reflectiveelements of the present invention are constituted of substantially-sametriangular lateral faces (faces c₁ and c₂) using the shared base edge(x, x, . . . ) as one side and two substantially-same quadrangularlateral faces (faces c₁ and b₁ and faces a₂ and b₂) substantiallyorthogonal to the lateral faces (faces c₁ and c₂) using two upper sidesof the lateral faces (faces c₁ and c₂) starting with apexes (H₁ and H₂)of the triangular-pyramidal reflective elements as one sides, sharingone ridge line of the triangular-pyramidal reflective elements, andusing the ridge line as one side.

As shown in FIG. 9, the negatively-tilted triangular-pyramidalreflective elements of the present invention shares a base edge (x, x, .. . ) on a base plane (X-X′) and they are faced each other to form thesubstantially-same element pair faced so as to be substantiallysymmetric and arranged in the closest-packed state at a repetitivepattern. However, because the base plane (X-X′) is located at a positionsubstantially upper than a horizontal plane (Z-Z′) serving as a commonplane, the shared base edges (x, x, . . . ) do not constitute acontinuous straight line through they are present on one straight lightbut they form a broken line broken every certain interval. Moreover,many base edges (x, x, . . . ) shared by a group of adjacent othertriangular-pyramidal reflective element pairs are parallel with thebroken straight line constituting the base edges (x, x, . . . ) to forma broken parallel straight-line group having equal repetitive pitches.

Therefore, though the lateral faces (faces c₁ and c₂) of thenegatively-tilted triangular-pyramidal reflective element of the presentinvention are faced each other by sharing base edges (x, x, . . . ), thebase edges (x, x, . . . ) do not constitute a continuous straight lineas described above but they form a broken line broken every certaininterval. Moreover, though faces c₁ are present on a virtual plane, theydo not form a continuous plane but they form independentsubstantially-isosceles-triangular strings arranged in the same patternevery certain interval. The same is true for the face c₂. A virtualplane including a string of faces c₁ and a virtual plane including astring of faces c₂ intersect each other at base edges (x, x, . . . ) andcross sections of them form a V-shaped groove and are faced each other.

To easily understand the present invention, FIG. 11 shows an enlargedtop view of a pair of negatively-tilted triangular-pyramidal reflectiveelements shown as the following patterns in FIG. 9 and FIG. 12 shows aside view from the arrow direction shown by the line L-L′ in FIG. 11.

FIGS. 11 and 12 are described below. The face c₁ of the right element R₁(that is, the element shown by the following pattern in FIG. 9) of apair of negatively-tilted triangular-pyramidal reflective elements ofthe present invention is a triangular plane surrounded by points H₁-D-E,the face a₁ is a quadrangular plane surrounded by points H₁-F₁-A-D, theface b₁ is a quadrangular plane surrounded by points H₁-F₁-B-E, thefaces a₁ and b₂ have the substantially same shape, and the faces c₁, a₁,and b₂ are substantially orthogonal to each other.

Moreover, the base plane of the right triangular-pyramidal reflectiveelement R₁ shown by a plane A-B-F₁ forms a part of the horizontal plane(Z-Z′) serving as a common plane.

In FIG. 12, the left triangular-pyramidal reflective element shown by R₂corresponds to the left triangular-pyramidal reflective element of theabove element pair shown by the following pattern in FIG. 9, the baseplane of the element is shown by A-B-F₂, the left triangular-pyramidalreflective element R₂ whose base plane is shown by A-B-F₂ has thesubstantially same shape as the right reflective element R₁ whose baseplane is shown by A-B-F₁ and located at the both sides of the base edge(D-E) (this is present on the shared base edge x in FIG. 3) shared bythe faces c₁ and c₂ of the both elements R₁ and R₂, and the left elementR₂ has a shape obtained by rotating the right element R₁counterclockwise by 180° about the middle point (O) of the base edge(D-E) shared by the both elements R₁ and R₂ on the base plane (X-X′).

Therefore, the face c₂ shown by points H₂-D-E of the left element R₂ inFIG. 11, the face b₂ shown by points H₂-F₂-A-D, and the face a₂ shown bypoints H₂-F₂-B-E have the substantially same shape and the faces c₂, a₂,and b₂ are also substantially orthogonal to each other.

Therefore, the height from the valley formed between lateral faces a₁and b₁ and lateral faces a₂ and b₂ of the negatively-tiltedtriangular-pyramidal reflective elements R₁ and R₂ of the presentinvention up to the apexes H₁ and H₂ is shown as h₀.

Moreover, as shown in FIGS. 11 and 12, the base edge D-E shared by thefaced faces c₁ and c₁ of the negatively-tilted triangular-pyramidalreflective elements R₁ and R₂ of the present invention is present on thebase plane (X-X′) and the height from the base plane (X-X′) up to theapexes H₁ and H₂ of the elements R₁ and R₂ is shown as h in FIG. 12.Furthermore, the height h corresponds to the depth of the V-shapedvalley formed by the faces c₁ and c₂ from the apexes H₁ and H₂ of theelements.

In the case of negatively-tilted triangular-pyramidal reflectiveelements of the present invention, base edges of the faces a₁ and a₂ ofthe elements R₁ and R₂ are present on a common line z as shown in FIGS.9 and 11, base edges of the faces b₁ and b₂ are located on a common linew, and base edges of the faces c₁ and c₂ are located on a common line x.

As shown in FIGS. 9 to 12, in the case of many negatively-tiltedtriangular-pyramidal reflective elements of the present invention, two cfaces to which the elements correspond share base edges (x, x, . . . )and they are faced each other and arranged on a substrate in theclosest-packed state.

A negatively-tilted triangular-pyramidal cube-corner retroreflectivesheeting of the present invention shown in FIGS. 9 to 12 is atriangular-pyramidal cube-corner retroreflective sheeting characterizedin that triangular-pyramidal cube-corner retroreflective elementsprotruded beyond a common base plane (X-X′) are faced each other andarranged in the closest-packed state by sharing one base edge on thebase plane (X-X′), the base plane (X-X′) is a common plane includingmany base edges (x, x, . . . ) shared by the triangular-pyramidalreflective elements, the two triangular-pyramidal reflective elementsfaced each other constitute an element pair having substantially sameshape faced so as to be respectively substantially symmetric to planes(Y-Y′, Y-Y′, . . . ) vertical to the base plane (X-X′) including manyshared base edges (x, x, . . . ) on the base plane (X-X′), thetriangular-pyramidal reflective elements are constituted ofsubstantially same triangular lateral faces (faces c₁ and c₂) using theshared base edges (x, x, . . . ) as one sides and substantially samequadrangular lateral faces (faces a₁ and b₁ and faces a₂ and b₂)substantially orthogonal to the face c₁ or the face c₂ by using uppertwo sides of the face c₁ or c₂ starting with apexes (H₁ and H₂) of thetriangular-pyramidal reflective elements as one sides and sharing oneridge line of the triangular-pyramidal reflective elements and using theridge line as one side, and when assuming the height from the apexes (H₁and H₂) of the triangular-pyramidal reflective elements up to the baseplane (X-X′) including the base edges (x, x, . . . ) of the triangularlateral faces (faces c₁ and c₂) of the triangular-pyramidal reflectiveelements as (h), the height from the apexes (H₁ and H₂) of thetriangular-pyramidal reflective elements up to a substantiallyhorizontal plane (Z-Z′) including base edges (z and w) of other lateralfaces (faces a₁ and b₂ and faces a₂ and b₂) of the triangular-pyramidalreflective elements as (h₀), the intersection between a vertical linefrom the apexes (H₁ and H₂) of the triangular-pyramidal reflectiveelements to the base plane (X-X′) and the base plane (X-X′) as P, theintersection between an optical axis passing through the apexes (H₁ andH₂) and the base plane (X-X′) as Q, and moreover, expressing distancesfrom the intersections (P) and (Q) up to planes (Y-Y′, Y-Y′, . . . )including the base edges (x, x, . . . ) shared by thetriangular-pyramidal reflective elements and vertical to the base plane(X-X′) as p and q, the optical axis tilts in a direction in which (q−p)becomes negative (−) and the above h and h₀ are not substantially equalto each other.

The present inventor et al. specified the tilt angle (θ) of aretroreflective sheeting constituted of the positively-tilted ornegatively-tilted triangular-pyramidal cube-corner retroreflectiveelements described above and the relation between the height (h₀) fromthe apexes (H₁ and H₂) up to the horizontal plane (Z-Z′) of the elementsand the height (h) up to the base plane (X-X′) and applied the patentsas described above (Japanese Patent Application Nos. 295907/1996 and330836/1997).

The present inventor et al. further continued the study. As a result,because we found that improvements in these two applications were notnecessarily sufficient, we further developed the idea of minimizing thedegree in which sizes of lateral faces (faces c₁ and c₂) are relativelyenlarged or contracted compared to other lateral faces (faces a₁ and b₂and faces a₂ and b₂) which is inevitably caused by a tilt of an opticalaxis and reached the present invention.

However, the present inventor et al. found that a triangular-pyramidalcube-corner retroreflective sheeting improved in entrance angularity andhaving a superior reflection brightness can be obtained when the ratio(h/h₀) between the height (h) from apexes (H₁ and H₂) of twotriangular-pyramidal reflective elements up to a base plane (X-X′)including base edges (x, x, . . . ) common to two faced lateral faces(faces c₁ and c₂) of these two elements and the height (h₀) from theapexes (H₁ and H₂) of the triangular-pyramidal reflective elements up toa substantially horizontal plane (Z-Z′) including base edges (z and w)of other lateral faces (faces a₁ and b₁ and faces a₂ and b₂) of thetriangular-pyramidal reflective elements meets a tilt angle θ of anoptical axis and a specific relational expression.

A triangular-pyramidal cube-corner retroreflective sheeting of thepresent invention is characterized in that the above height ratio (h/h₀)meets a tilt angle (θ) of an optical axis and the following relationalexpression (1). $\begin{matrix}{{0.5\quad R} \leqq \frac{h}{h_{0}} \leqq {1.5\quad R}} & (1)\end{matrix}$

(In the above expression, R denotes a value defined by the followingexpression.)$R = \frac{{\sin \left( {35.2644^{*} - \theta} \right)} + {1.2247\sin \quad \theta}}{\sin \left( {35.2644^{*} - \theta} \right)}$

{In the above expression, it is assumed that when the above(q−p)has anegative (−) value, θ takes a negative (−) value.}

In the above expression (1), when (h/h₀) has a very small value such asless than 0.5R, this is not preferable because the unbalance betweenareas of faces c, a, and b is insufficiently improved and the frontbrightness of an obtained retoreflective sheeting is low, and theentrance anguarity is insufficiently improved. However, when (h/h₀) hasa very large value exceeding 1.5R, this is not preferable because theinbalance between areas of faces c, a, and b is excessively improved. Inthe case of a positive tilt, the face c becomes extremely larger thanthe faces a and b. In the case of a negative tilt, the face c becomesextremely smaller than the faces a and b. This is not preferable becausethe front brightness of an obtained retroreflective sheeting is low andthe entrance angularity is insufficiently improved similarly to the caseof less than 0.5R.

In the above expression (1), it is preferable that (h/h₀) is kept in thefollowing range. $\begin{matrix}{{0.6R}\quad \leqq \quad \frac{h}{h_{0}} \leqq \quad {1.4R}} & (2)\end{matrix}$

It is more preferable that (h/h₀) is kept in the following range.$\begin{matrix}{{0.8R}\quad \leqq \quad \frac{h}{h_{0}} \leqq \quad {1.2R}} & (3)\end{matrix}$

It is particularly preferable that (h/h₀) is kept in the followingrange. $\begin{matrix}{{0.85R}\quad \leqq \quad \frac{h}{h_{0}} \leqq \quad {1.15R}} & (4)\end{matrix}$

R in the above expressions is defined by the above expression (1) (ordefined by claim 1).

The present inventor et al. knew that it was more preferable that therate of the difference between the value of (h−h₀)/h₀, that is, theheight (h₀) from apexes (H₁ and H₂) of a triangular-pyramidal reflectiveelement pair up to a horizontal plane (Z-Z′) and the height (h) up to abase plane (X-X′) to the height (h₀), in other words, the relationbetween a deep groove or the degree of the deep groove and a tilt angle(θ) meets the following expression (5) and it was particularlypreferable that the rate meets the following expressions (5) and (6).$\begin{matrix}{{0.3\left( {R - 1} \right)} \leqq \frac{h - h_{0}}{h_{0}} \leqq {1.5\left( {R - 1} \right)}} & (5) \\{{0.4\left( {R - 1} \right)} \leqq \frac{h - h_{0}}{h_{0}} \leqq {1.2\left( {R - 1} \right)}} & (6)\end{matrix}$

(In the above expressions (5) and (6), D denotes a value defined by thefollowing expression.)$D = {{R - 1} = \frac{1.2247\quad \sin \quad \theta}{\sin \left( {35.2644^{*} - \theta} \right)}}$

A positively- or negatively-tilted triangular-pyramidal cube-cornerretroreflective sheeting of the present invention is preferable in whichthe optical axis of a triangular-pyramidal reflective element pair tiltsby 3 to 15° from a vertical plane (Y-Y′) in a direction in which thedifference (p−q) between the distance (p) from the intersection (P)between a vertical line extended from apexes (H₁ and H₂) of atriangular-pyramidal reflective element pair to a horizontal plane(Z-Z′) and the horizontal plane (Z-Z′) up to vertical planes (Y-Y′,Y-Y′, ) including base edges (x, x, . . . ) shared by the element pairand the distance (q) from the intersection (Q) between the optical axisof the triangular-pyramidal reflective element pair and the horizontalplane (Z-Z′) up to the planes (Y-Y′, Y-Y′, . . . ) vertical to the baseplane (X-X′) including base edges (x, x, . . . ) shared by the elementpair becomes positive or negative.

In the case of the present invention, when referring to FIGS. 8 to 12, acube-corner retroreflective sheeting is preferable in which an angle (θ)from a vertical line (H₁-P) to the horizontal plane (Z-Z′) {this can bealso considered as a plane (Y-Y′) vertical to the base plane (X-X′)}from the apex H₁, of the triangular-pyramidal reflective element R₁ isreferred to as an optical-axis tilt angle and the optical axis passingthrough the apex H₁ tilts in a direction in which the above (p−q)becomes positive or negative so that the optical-axis tilt angle (θ)ranges between 4 and 12°, particularly a triangular-pyramidalcube-corner retroreflective sheeting is preferable in which the opticalaxis tilts by 5° to 10° from the vertical plane (Y-Y′) in a direction inwhich the above (p−q) becomes positive or negative.

In the case of positively-tilted triangular-pyramidal reflectiveelements of the present invention, the height (h) from the apexes (H₁and H₂) of the reflective elements up to the base plane (X-X′) includingbase edges (x, x, . . . ) shared by the element pair is substantiallylarger than the height (h₀) from the apexes (H₁ and H₂) of thetriangular-pyramidal reflective elements the substantially horizontalplane (Z-Z′) substantially including base edges (z and w) as shown inFIG. 8. Therefore, various optical characteristics are improved.

The above improvement can be realized because h is substantially largerthan h₀ and thereby, it is possible to increase the area of the face c₁compared to the area of the lateral face c₁ of the prior art in which his equal to h₀. Particularly, in the case of light almost-verticallyentering the face c₁, in other words, light having a large entranceangle, the entrance angularity is remarkably improved because the areaof the face c₁ is increased.

In the case of a negatively-tilted triangular-pyramidal reflectiveelements of the present invention, the height (h) from apexes (H₁and H₂)of the reflective elements up to the base plane (X-X′) including baseedges (x, x, . . . ) shared by the element pair is substantially smallerthan the height (h₀) from the apexes (H₁ and H₂) of thetriangular-pyramidal reflective elements up to the substantiallyhorizontal plane (Z-Z′) including base edges (z and w). Therefore,various optical characteristics are improved.

The above improvement can be realized because h is substantially smallerthan h₀ and thereby it is possible to decrease the area of the face c₁compared to the area of the lateral face c₁ of the conventional art inwhich h is equal to h₀, in other words, it is possible to make the areaof the face a₁ relatively larger than that of the face b₁. Particularly,in the case of light almost vertically entering the faces a₁ and b₁, inother words, light having a large entrance angle, the entranceangularity is remarkably improved because areas of the faces a₁ and b₂are increased.

In the case of the present invention, the entrance angularity isimproved because an optical axis tilts so that the above (q−p) becomespositive or negative. A triangular-pyramidal reflective element with anoptical axis tilted according to the prior art has disadvantages that anormal triangular-pyramidal reflective element with an optical axis nottilted tilts its optical axis so that the above (q−p) becomes positiveor negative, thereby areas of lateral faces (faces c₁ and c₂) having acommon base edge (x) are decreased compared to areas before tilted inpositive tilt but increases in negative tilt, the difference betweensizes of two other faces a₁ and b₂ becomes remarkable, and theprobability of causing three-face reflection and then retroreflection isdeteriorated. For the incoming light to reflect from three tilted sidefaces and efficiently retroreflect, it is preferable that areas of threelateral faces are equal to each other as described above. In the case ofa tilted triangular-pyramidal reflective element of the prior art,however, the probability of causing three-face reflection and thenretroreflection described above is deteriorated because the differencebetween areas of lateral faces (faces c₁ and c₂) having a common baseedge becomes remarkable compared to the case of two other faces (face a₁and b₁ and faces a₂ and b₂) as a tilt angle increases. Therefore, notonly the retroreflective performance of the light incoming from thefront (front reflection brightness) is deteriorated but also theretroreflective performance when an entrance angle increases (entranceangularity) is deteriorated.

When an optical axis tilts so that (p−q) becomes positive (+), areas oflateral faces (faces c₁ and c₂) of a triangular-pyramidal reflectiveelement decreases to approx. 91% when an optical-axis tilt angle (θ) is+3°, to approx. 86% when the tilt angle (θ) is +4°, and to approx. 62%when the tilt angle (θ) is +12°, compared to areas before the opticalaxis tilts. When the optical axis tilts so that (p−q) becomes negative(−), areas of lateral faces (faces a₁ and b₁ and faces a₂ and b₂)decreases to approx. 90° when an optical-axis tilt angle (θ) is −3°, toapprox. 87% when the tilt angle (θ) is −4°, and to approx. 65% when thetilt angle (θ) is −12°, compared to areas before the optical axis tilts.

In the case of positively-tilted triangular-pyramidal reflectiveelements of the present invention, however, it is possible to increaseareas of lateral faces (faces c₁ and c₂) compared to areas of tiltedside faces of a triangular-pyramidal reflective elements formed inaccordance with the prior art because the positively-tiltedtriangular-pyramidal reflective elements are designed so that the height(h) from apexes (H₁ and H₂) up to a base plane (X-X′) is substantiallylarger than the height (h₀) up to a horizontal plane (Z-Z′). In the caseof negatively-tilted triangular-pyramidal reflective elements of thepresent invention, however, it is possible to increase areas of twolateral faces (faces a₁ and b₁ and faces a₂ and b₂) compared to tiltedside faces of triangular-pyramidal reflective elements formed inaccordance with the prior art because the negatively-tiltedtriangular-pyramidal reflective elements are designed so that the height(h) from apexes (H₁ and H₂) up to a base plane X-X′) is substantiallysmaller than the height (h₀) up to a horizontal plane (Z-Z′).

Thus, a triangular-pyramidal reflective element of the present inventionparticularly makes it possible to improve the disadvantage thatbrightness is deteriorated due to the unbalance between areas of facesa, b, and c of the element caused by tilting an optical axis so that itstilt angle (θ) indicates 3° to 15° in a direction in which (p−q) becomesnegative (−) or positive (+).

Because of the above reason, in the case of the present invention, it ispreferable to tilt an optical axis so that its tilt angle (θ) indicates40° to 12°, preferably 5° to 10° in a direction in which (q−p) becomesnegative (−) or positive (+). In the case of a triangular-pyramidalreflective element in which its optical axis tilts by an angle exceeding15° in a direction in which the tilt angle (θ) of the optical axisbecomes negative (−) or positive (+), the element is excessivelydeformed and thereby, the rotation angularity tends to deterioratebecause reflection brightness greatly depends on the direction of lightentering the element (rotation angle).

It is preferably recommended that the height (h₀) from apexes (H₁ andH₂) of triangular-pyramidal reflective elements of the present inventionup to a horizontal plane (Z-Z′) ranges between 50 and 400 μm, morepreferably between 60 and 200 μm. When the height (h₀) is less than 50μm, the size of an element becomes too small and thereby, divergence ofretroreflected light is excessively increased due to the diffractioneffect determined by a bottom opening area of an element and the frontbrightness characteristic tends to deteriorate. Moreover, when theheight (h₀) exceeds 400 μm, the thickness of a sheeting becomesexcessive and thereby, a flexible sheeting cannot be easily obtained.

Furthermore, three prism face angles formed by the fact that threelateral faces (faces a₁, b₁, and c₁) or (faces a₂, b₂, and c₂) servingas prism faces of a triangular-pyramidal reflective element of thepresent invention intersect each other substantially becomes rightangles. However, it is not always necessary that they are strictly rightangles. It is also possible to provide a very small angle deviation fromright angle according to necessity. By providing a very slight angledeviation for the prism face angles, it is possible to properly emanatethe light reflected from an obtained triangular-pyramidal reflectiveelement. However, when excessively increasing the angle deviation, theretroreflective performance is deteriorated because the light reflectedfrom the obtained triangular-pyramidal reflective element extremelyemanates. Therefore, it is preferable to keep at least one prism faceangle formed when these three lateral faces (faces a₁, b₁, and c₁ orfaces a₂, b₂, and c₂) intersect each other generally in a range of 89.5°to 90.5°, preferably in a range of 89.7° to 90.3°.

It is possible to generally manufacture a triangular-pyramidalcube-corner retroreflective sheeting of the present invention by using acube-corner molding die in which shapes of the above-describedtriangular-pyramidal reflective elements are arranged on a metallic beltin the closest-packed state as inverted concave shapes and thereby,thermally pressing a proper flexible resin sheeting superior in opticaltransparency and uniformity to be described later against the moldingdie and inversely transferring the die shape to the resin sheeting.

A typical manufacturing method of the above cube-corner molding die isdisclosed in, for example, the above Stamm's U.S. Pat. No. 3,712,707 indetail and it is possible to adopt a method conforming to the abovemethod for the present invention.

Specifically, parallel grooves having the same depth (h₀) and a V-shapedsectional form is cut on a substrate whose surface is flatly ground byusing a carbide cutting tool having a point angle of 73.4 to 81.0° forpositive tilt or having a point angle of 66.4 to 537° for negative tilt(e.g. diamond cutting tool or tungsten-carbide cutting tool) and therebydeciding a repetitive pitch, a groove depth (h₀), and a mutual crossingangle in accordance with the shape of a purposed triangular-pyramidalreflective element in two directions (z direction and w direction inFIG. 3) and then, a microprism mother die is formed in which convexvery-small triangular pyramids are arranged in the closest-packed stateby using a carbide cutting tool having a point angle of 64.5 to 46.5°for positive tilt and having a point angle of 78.5 to 100.5° fornegative angle and thereby cutting a V-shaped parallel groove at arepetitive pitch (repetitive pitch of line x in FIG. 3) passing throughthe intersection between the formed z-directional groove andw-directional groove and bisecting a supplementary angle of the crossingangle of these two directions (in this case, the acute angle is referredto as “crossing angle”) in the third direction (x direction). In thiscase, the present invention performs cutting by adjusting the depth (h₀)of the x-directional groove so that it is deeper than the depth (h₀) ofthe z- and w-directional grooves for positive tilt and shallower thanthe depth (h₀) of the z-and w-directional grooves for negative tilt.

In the case of a preferred mode of a positively-tilted reflectiveelement of the present invention, the z- and w-directional repetitivepitch ranges between 100 and 810 μm, the groove depth (h₀) rangesbetween 50 and 400 μm, the mutual crossing angle ranges between 43 and55°, and the x-directional groove depth (h₀) ranges between 75 and 600μm. In the case of a preferred mode of a negatively-tilted reflectiveelement, a z- and w-directional repetitive pitch ranges between 104 and992 μm, the groove depth (h₀) ranges between 50 and 400 μm, the mutualcrossing angle ranges between 64.7 and 75.1°, and the x-directionalgroove depth (h₀) ranges between 33 and 380 μm.

Cutting of x-, w-, and z-directional grooves is generally performed sothat the cross section of each groove becomes isosceles triangular.However, it is also possible to cut these three directional grooves sothat the cross section of at least one-directional groove is slightlydeviated from an isosceles triangular shape. A method of cutting agroove by using a cutting tool whose front-end shape is asymmetric toright and left or a method of cutting a groove by slightly tilting acutting tool symmetric to right and left can be listed. Thus, byslightly shifting the cross section of a groove from an isoscelestriangular shape, it is possible to provide an angle deviation slightlydeviated from right angle (90°) for at least one of prism face angles ofthree lateral faces (faces a₁, b₁, and c₁ or faces a₂, b₂, and c₂) of anobtained triangular-pyramidal reflective element and thereby, it ispossible to properly emanate the light reflected from atriangular-pyramidal reflective element from a complete retroreflectivedirection.

It is preferable to use a metal having a Vickers hardness (JIS Z 2244)of 350 or more, particularly 380 or more as a substrate which can bepreferably used to form the above microprism mother die. Specifically,amorphous copper, electrodeposited nickel, or aluminum can be used asthe substrate. Moreover, a copper-zinc alloy (brass), copper-tin-zincalloy, nickel-cobalt alloy, nickel-zinc alloy, or aluminum alloy can beused as the substrate.

It is also possible to use a synthetic resin as the above substrate. Itis preferable to use a material made of a synthetic resin having a glasstransition point of 150° C. or higher, particularly 200° C. or higherand a Rockwell hardness (JIS Z 2245) of 70 or more, particularly 75 ormore as the above substrate because a synthetic resin does not easilycause a trouble that the resin is softened under cutting to makehigh-accuracy cutting difficult. Specifically, one of the followingmaterials can be used: polyethylene-terephthalate-based resin,polybutylene-phthalate-based resin, polycarbonate-based resin,polymethyl-methacrylate-based resin, polyimide-based resin,polyarylate-based resin, polyhether-sulfone-based resin,polyetherimide-based resin, and cellulose-triacetate-based resin.

To form a flat plate by one of the above synthetic resins, it ispossible to use the normal resin forming method such as extrusionmolding method, calender molding method, or solution casting method andmoreover perform heating and extending according to necessity. Thus, itis possible to apply the preparatory conduction treatment to the planeof the flat plate thus formed in order to simplify the conductiontreatment and/or electroforming for forming an electroforming die from aprism mother die formed in accordance with the above method. For thepreparatory conduction treatment, one of the following methods can beused: vacuum evaporation method for vacuum-evaporating such metals asgold, silver, copper, aluminum, zinc, chromium, nickel, and selenium;cathode sputtering method using the above metals, and electrolessplating method using copper or nickel. Moreover, it is allowed to makethe flat plate conductive by mixing conductive impalpable powder such ascarbon black or the like or organometallic salt into a synthetic resin.

Then, the surface of the obtained microprism mother die is electroformedand a metallic film is formed. By removing the metallic film from thesurface of the mother die, it is possible to form a metallic die forforming a triangular-pyramidal cube-corner retroreflective sheeting ofthe present invention.

In the case of a metallic mother die, it is possible to electroform themother die immediately after cleaning the surface of the die accordingto necessity. In the case of a synthetic-resin microprism mother die,however, it is necessary to apply conduction treatment to the prismsurface of the mother die in order to make the surface conductive beforeelectroforming the mother die. As the conduction treatment, it ispossible to use silver mirroring, electroless plating, vacuumevaporation, or cathode sputtering.

Specifically, as the above silver mirroring, a method can be used inwhich the surface of a mother die formed in accordance with the abovemethod is cleaned with an alkaline detergent to remove contaminationsuch as oil component and the like, then activated by a surface-activeagent such as tannic acid, and then silver-mirrored by a silver-nitrateaqueous solution. The silver mirroring can adopt the spraying methodusing a two-cylinder nozzle gun storing a silver-nitrate aqueoussolution and a reducing agent (grape sugar or glyoxal) aqueous solutionor the dipping method for dipping an object in a mixed solution of asilver-nitrate aqueous solution and a reducing-agent aqueous solution.Moreover, it is preferable that a silver-mirrored film has a thicknessas small as possible in a range in which the conductivity underelectroforming is satisfied such as a thickness of 0.1 μm.

Electroless plating uses copper or nickel. An electroless nickel platingsolution can use nickel sulfate or nickel chloride as water-solublemetallic salt of nickel. A plating solution is used which is obtained byadding a solution mainly containing citrate and malate respectivelyserving as a complexing agent, and sodium hypophosphite, boronizedhydrogen sodium, and amine borane respectively serving as a reducingagent to the electroless nickel plating solution.

Vacuum evaporation can be performed by cleaning the surface of a motherdie, then putting the die in a vacuum system, thermally evaporatinggold, silver, copper, aluminum, zinc, nickel, chromium, and selenium,precipitating them on the cooled mother-die surface, and forming aconductive film. Moreover, cathode sputtering can be performed byputting a mother die treated similarly to the case of the vacuumevaporation in a vacuum system in which a cathode plate capable ofmounting a smooth and desired metallic foil and an anode table made of ametal such as aluminum or iron for mounting a material to be treated andsetting the mother die on the anode table, setting a metallic foil sameas that used for the vacuum evaporation to a cathode and electrifyingthe foil to cause glow discharge, making an anode-ion flow generated bythe glow discharge collide with the cathode metallic foil and therebyevaporating metallic atoms or particles, precipitating the metallicatoms or particles on the surface of the mother die, and forming aconductive film. The thickness of a conductive film formed by one of theabove methods is 30 nm.

To form a smooth and uniform electroformed layer on a prism mother diemade of a synthetic resin through electroforming, it is necessary touniformly apply conduction treatment to the entire surface of the motherdie. When conductive treatment is uniformly performed, a trouble mayoccur that the smoothness of the surface of the electroformed layer at aportion inferior in conductivity is deteriorated or no electroformedlayer is formed but a defective portion is formed.

To avoid the above trouble, it is possible to use a method of improvingthe wetness of a silver-mirrored film by treating a treatment face witha solvent such as alcohol immediately before silver mirroring. However,because a synthetic-resin prism mother die formed for the presentinvention has a very deep acute-angle concave portion, wetness tends tobe incompletely improved. The trouble of a conductive film due to theconcave portion also easily occurs in vacuum evaporation.

To uniform the surface of an electroformed layer obtained throughelectroforming, activation is frequently performed. The activation canuse a method of dipping an object in a 10-wt % sulfamic-acid aqueoussolution.

When electroforming a silver-mirrored synthetic-resin mother die, asilver layer is integrated with an electroformed layer and easilyseparated from the synthetic-resin mother die. However, when forming aconductive film made of nickel or the like through electroless platingor cathode sputtering, it may be difficult to separate an electroformedlayer from a synthetic-resin layer after electro-forming because thesynthetic-resin surface easily closely-contacts with the conductivefilm. In this case, it is preferable to apply the so-called separationtreatment such as chromate treatment onto the conductive layer beforeelectroforming. In this case, the conductive layer remains on thesynthetic-resin layer after separated.

The synthetic-resin prism mother die on which the conductive film isformed undergoes the above various pretreatments and then, anelectroformed layer is formed on the conductive film throughelectroforming. In the case of metallic prism mother die, the surface ofthe die is cleaned according to necessity and then, an electroformedlayer is directly formed on the metal.

Electroforming is generally performed in a 60-wt % nickel-sulfamateaqueous solution at 40° C. and a current of approx. 10 A/dm². A uniformelectroformed layer is easily obtained by setting an electroformed-layerforming rate to, for example, 48 hr/mm or less. However, at a formingrate of more than 48 hr/mm, a trouble easily occurs that the surfacesmoothness is deteriorated or a defective portion is easily formed in anelectroformed layer.

In the case of electroforming, it is also possible to performnickel-cobalt-alloy electroforming to which a component such as cobaltis added in order to improve the die-surface abrasion characteristic. Byadding 10 to 15 wt % of cobalt, it is possible to improve the Vickershardness Hv of an obtained electroformed layer up to 300 to 400.Therefore, it is possible to form a synthetic resin by an obtainedelectroformed die and improve the durability of the die in order tomanufacture a triangular-pyramidal cube-corner retroreflective sheetingof the present invention.

A first-generation electroforming die thus formed from a prism motherdie can be repeatedly used as an electroforming master used to form asecond-generation electroforming die. Therefore, it is possible to formmany electroforming dies from one prism mother die.

A plurality of electroforming dies formed are precisely cut, combinedand joined up to a final die size for forming a microprism sheeting andused. To join the electroforming dies, it is possible to use a method ofmerely butting cut end faces each other or a method of welding combinedjoints through electron-beam welding, YAG laser welding, orcarbon-dioxide laser welding.

A combined electroforming die is used to mold a synthetic resin as asynthetic-resin molding die. As the synthetic-resin molding method, itis possible to use compression molding or injection molding.

Compression molding can be performed by inserting a formed thin-wallnickel electroforming die, a synthetic-resin sheeting having apredetermined thickness, and a silicon-rubber sheeting having athickness of approx. 5 mm as a cushion material into acompression-molding press heated to a predetermined temperature, thenpreheating them at a pressure of 10 to 20% of a molding pressure for 30sec, and then heating and pressing them for approx. 2 min under acondition of 10 to 30 kg/cm². Thereafter, it is possible to obtain aprism molding product by lowering the temperature up to room temperaturewhile pressed and releasing the pressure.

Moreover, it is possible to obtain a continuous-sheetinglike product byjoining a thin-wall electroforming die having a thickness of approx. 0.5mm formed by the above method through the above welding method to forman endless belt die, setting the belt die on a pair of rollersconstituted of a heating roller and a cooling roller and rotating thebelt die, supplying melted synthetic resin in the form of a sheeting topressure-mold the melted synthetic resin with one silicone roller ormore and then, cooling the resin to the glass transition point or loweron the cooling roller, and separating the resin from the belt die.

Then, a negatively-tilted triangular-pyramidal cube-cornerretroreflective sheeting which is one mode of a preferred structure of atriangular-pyramidal cube-corner retroreflective sheeting of the presentinvention is described below by referring to FIG. 13 showing a sectionalview of the negatively-tilted triangular-pyramidal cube-cornerretroreflective sheeting.

In FIG. 13, symbol (1) denotes a reflective element layer in whichtriangular-pyramidal reflective elements (R₁ and R₂) of the presentinvention are arranged in the closest-packed state, (2) denotes a holderlayer for holding the reflective elements, and (10) denotes a lightentrance direction. Though the reflective element layer (1) and holderlayer (2) are normally united into one body, it is also allowed tosuperpose separate layers each other. Correspondingly to the purpose andworking environment of a retroreflective sheeting of the presentinvention, it is possible to form a surface protective layer (4), aprinting layer (5) for communicating information to an observer orcoloring a sheeting, a binder layer (6) for achieving anenclosing-sealing structure for preventing moisture from entering theback of a reflective element layer, an air layer (3) enclosed by thereflective element layer (1) and binder layer (6) to assureretroreflection at an interface between reflective elements, a supportlayer (7) for supporting the binder layer (6), an adhesive layer (8)used to attach the retroreflective sheeting to other structure, and aseparating-material layer (9).

It is possible to use the same resin as that used for theretroreflective element layer (1). Moreover, to improve the weatherresistance, it is possible to use an ultraviolet absorbent, lightstabiizer, and antioxidant independently or by combining them. Moreover,it is possible to add various organic pigments, inorganic pigments, anddyes as colorants.

It is generally possible to set the printing layer (5) between thesurface protective layer (4) and holder layer (2) or on the surfaceprotective layer (4) or the reflection face of a reflective element (1)by means of gravure printing, screen printing, or ink jet printing.

Though any material can be used as a material constituting thereflective element layer (1) and holder layer (2) as long as thematerial meets flexibility which is one of the objects of the presentinvention, it is preferable to use a material having opticaltransparency and uniformity. The following materials can be used for thepresent invention: olefin resins such as polycarbonate resin, vinylchloride resin, (meth)acrylic resin, epoxy resin, styrene resin,polyester resin, fluorine resin, and polypropylene resin;cellulose-based resins; and urethane resin.

It is general to set the air layer (3) to the back of a cube-cornerretroreflective element in order to increase a critical angle formeeting an internal total-reflection condition. It is preferable thatthe reflective element layer (1) and support layer (7) are enclosed andsealed by the binder layer (6) in order to prevent such troubles asdecrease of a critical angle and corrosion of a metal layer due tomoisture under a working condition. The above enclosing and sealingmethod can use one of the methods disclosed in the UP Pat. Nos.3,190,178 and 4,025,159 and Japanese Utility Model Laid-Open No.28669/1975. It is possible to use one of the resins such as(meth)-acrylic resin, polyester resin, alkyd resin, and epoxy resin forthe binder layer (6). As a joining method, it is possible to properlyuse the publicly-known thermal-fusion-resin joining method,thermosetting-resin joining method, ultraviolet-curing-resin joiningmethod, or electron-beam-curing-resin joining method.

It is possible to apply the binder layer (6) to the entire surface ofthe support layer (7) and selectively set the layer (6) to a joint witha retroreflective element layer by a method such as the printing method.

It is possible to use a resin constituting a retroreflective element,general film-moldable resin, fiber, cloth, metallic foil of stainlesssteel or aluminum, or plate as a material constituting the support layer(7) independently or by combining them.

As the adhesive layer (8) used to attach a retroreflective sheeting ofthe present invention to a metallic plate, wooden plate, glass plate, orplastic plate and the separating-material layer (9), it is possible toproperly select a publicly-known material.

The present invention is more minutely described below by referring toembodiments and comparative examples.

Embodiment 1

A parallel groove having a V-shaped cross section was cut on a brassplate of 50-mm square whose surface was flatly ground through the flycutting method at a repetitive pattern in the first direction (zdirection in FIG. 5) and the second direction (w direction in FIG. 5) byusing a diamond cutting tool having a point angle of 77.04° so that thefirst- and second-directional repetitive pitch is 169.70 μm, the groovedepth (h₀) is 80.00 μm, and the crossing angle between lines z and wshown by <A-K₁-B in FIG. 7 becomes 50.68°.

Thereafter, a V-shaped groove was cut in the third direction (xdirection) by using a diamond cutting tool having a point angle of56.53° so that the repetitive pitch (repetitive pitch of line x in FIG.3) was 198.26 μm, the groove depth (h₀) was 92.00 μm, and the crossingangle between the first and second directions on one hand and the thirddirection on the other became 64.66° to form a mother die obtained byarranging many convex positively-tilted triangular-pyramidalretroreflective elements in which the height (h₀) from the horizontalplane (Z-Z′) of triangular-pyramidal reflective elements up to theapexes (H₁ and H₂) of the triangular-pyramidal reflective elements was80.00 μm and the height (h₀) from the base plane (X-X′) up to the apexes(H₁ and H₂) of the triangular-pyramidal reflective elements was 92.00 μmon a brass plate in the closest-packed state. The optical-axis tiltangle of the triangular-pyramidal retroreflective element was +7°.Moreover, because h/h₀ is 92/80=1.15, (h−h₀)/h₀ becomes 0.15. Moreover,$R = {\frac{{\sin \left( {35.2644^{*} - \theta} \right)} + {1.2247\quad \sin \quad \theta}}{\sin \left( {35.2644^{*} - \theta} \right)} = 1.315}$

Therefore, D=R−1=0.315 was obtained. From these facts, obtainedtriangular-pyramidal reflective elements showed h/h₀=0.875R and(h−h₀)/h₀=0.476.

A concave cube-corner-molding die which was made of nickel and whoseshape was inverted was formed through electroforming by using the abovebrass mother die. A triangular-pyramidal cube-corner retroreflectivesheeting made of polycarbonate was formed on whose surfacepositively-tilted triangular-pyramidal retroreflective elements in whichthe thickness of a support layer was approx. 150 μm, h₀ was 80 μm and hwas 92 μm, and an angle deviation was not provided for prism face anglesof three faces constituting a triangular pyramid were arranged in theclosest-packed state by using the above molding die and thereby,compression-molding a polycarbonate-resin sheeting (“IUPILON E2000 madeby Mitsubishi Engineering Plastics Corp.) having a thickness of 230 μmat a molding temperature of 200° C. and a molding pressure of 50 kg/cm²,then cooling the sheeting up to 30° C. under a pressure, and then takingout the sheeting.

Embodiment 2

A mother die obtained by arranging many convex triangular-pyramidal cubecorners in which the height (h₀) from the horizontal plane (Z-Z′) oftriangular-pyramidal reflective elements was 80.00 μm and the height(h₀) from the base plane (X-X′) up to apexes (H₁ and H₂) of thetriangular-pyramidal reflective elements was 64.00 μm in theclosest-packed state was formed on a brass plate similarly to the caseof the embodiment 1 except that cutting was performed through the flycutting method along the first direction (z direction) and the seconddirection (w direction) by using a diamond cutting tool having a pointangle of 63.11° so that the first- and second-directional repetitivepitch was 149.33 μm, the cut-groove depth (h₀) was 80.00 μm, and thecrossing angle between the first and second directions became 67.85°instead of performing cutting along the first direction (z direction)and the second direction (w direction) by using a diamond cutting toolhaving a point angle of 77.04° so that the first- and second-directionalrepetitive pitch was 169.70 μm, the groove depth (h₀) was 80.00 μm, andthe crossing angle between the first and second directions became 50.68°and cutting was performed by using a diamond cutting tool having athird-directional (x-directional) point angle of 84.53° so that therepetitive pitch was 146.19 μm, the cut-groove depth was 64.00 μm, andthe crossing angle between the first and second directions on one handand the third direction on the other became 56.08° instead of cutting aV-shaped parallel groove by using a diamond cutting tool having athird-directional (x-directional) point angle of 56.53° so that therepetitive pitch was 198.26 μm, the groove depth (h) was 92.00 μm, andthe crossing angle between the first and second directions on one handand the third direction on the other became 64.66°. The optical-axistilt angle θ of the triangular-pyramidal reflective element was equal to−7°. Moreover, h/h₀ was equal to 64/80=0.80, (h−h₀)/h₀ was equal to−0.20, R was equal to 0.7781, and D was equal to R−1=−0.2219. From thesefacts, an obtained triangular-pyramidal reflective element showedh/h₀=1.028R and (h−h₀)/h₀=0.901D.

Then, similarly to the case of the embodiment 1, a concavecube-corner-molding die made of nickel was formed by using the die and atriangular-pyramidal cube-corner retroreflective sheeting made ofpolycarbonate resin was formed on whose surface negatively-tiltedtriangular-pyramidal retroreflective elements in which the thickness ofa support layer was approx. 150 μm, h₀ was 80 μm and h was 64 μm, and anangle deviation was not provided for prism face angles of three facesconstituting a triangular pyramid were arranged in the closest-packedstate.

Comparative Example 1

A mother die obtained by arranging many convex triangular-pyramidal cubecorners in which the height (h₀=h) of a cube-corner retroreflectiveelement was 80.00 μm on a brass plate in the closest-packed state wasformed similarly to the case of the embodiment 1 except that cutting wasperformed through the fly cutting method so that the first- andsecond-directional repetitive pitch became 164.18 μm instead ofperforming cutting through the fly cutting method so that the first- andsecond-directional repetitive pitch became 169.70 μm and cutting wasperformed so that the third-directional (x-directional) repetitive pitchbecame 191.81 μm and the cut-groove depth (h) became 80.00 μm instead ofcutting a V-shaped parallel groove so that the third-directional(x-directional) repetitive pitch became 198.26 μm and the groove depth(h) became 92.00 μm. The optical-axis tilt angle θ of the reflectiveelement was +7° and prism face angles of three faces constituting atriangular pyramid were all 90°.

Thereafter, a concave cube-corner molding die made of nickel was formedsimilarly to the case of the embodiment 1 and thereby, apolycarbonate-resin sheeting same as the case of the embodiment 1 wascompression-molded under the molding condition same as the case of theembodiment 1 to form a triangular-pyramidal cube-corner retroreflectivesheeting made of polycarbonate resin on whose surface positively-tiltedtriangular-pyramidal retroreflective elements in which the thickness ofa support layer was approx. 150 μm, h₀ was equal to h=80 μm and an angledeviation was provided for prism face angles of three faces constitutinga triangular pyramid were arranged was formed.

Comparative Example 2

A mother die obtained by arranging many convex triangular-pyramidal cubecorners in which the height (h₀=h) of a cube-corner retroreflectiveelement was 80.00 μm were arranged on a brass plate in theclosest-packed state was formed similarly to the case of the embodiment1 except that cutting was performed through the fly cutting method byusing a diamond cutting tool having a point angle of 63.11° so that thefirst- and second-directional repetitive pitch became 179.40 μm and thecrossing angle between the first and second directions became 67.85°instead of performing cutting through the fly cutting method in thefirst (z direction) and second direction (w direction) by using adiamond cutting tool having a point angle of 77.04° so that the first-and second-directional repetitive pitch became 169.70 μm and thecrossing angle between the first and second directions became 50.68° andperforming cutting by using a diamond cutting tool having athird-directional (x-directional) point angle of 84.53° so that therepetitive pitch became 160.73 μm and the cut-groove depth (h) became80.00 μm, and the crossing angle between the first and second directionson one hand and the third direction on the other became 56.08° insteadof performing cutting a V-shaped groove by using a diamond cutting toolhaving a third-directional (x-directional) point angle of 56.53° so thatthe repetitive pitch became 198.26 μm, the groove depth (h) became 92.00μm, and the crossing angle between the first and second directions onone hand and the third direction on the other became 64.66°. Theoptical-axis tilt angle θ of the reflective element was −7 and prismface angles of three faces constituting a triangular pyramid were all90°.

Hereafter, similarly to the case of the embodiment 1, a concavecube-corner molding die made of nickel was formed and thereby, apolycarbonate-resin sheeting same as the case of the embodiment 1 wascompression-molded under the same molding condition as the case of theembodiment 1 to form a triangular-pyramidal cube-corner retroreflectivesheeting made of polycarbonate on whose surface negatively-tiltedtriangular-pyramidal retroreflective elements in which the thickness ofa support layer was approx. 150 μm, h₀ was equal to h=80 μm, and anangle deviation was not provided for prism face angles of three facesconstituting a triangular pyramid were arranged in the closest-packedstate.

Table 1 shows measured data for retroreflection brightness oftriangular-pyramidal cube-corner retroreflective sheetings formed forthe above embodiments 1 and 2 and comparative examples 1 and 2. Theretroreflective sheetings of the embodiments 1 and 2 showed a highreflection brightness in a wide range. However, the reflective sheetingof the comparative example 1 has a particularly large brightness changeat an entrance angle of 50 to 100 and the reflective sheeting of thecomparative example 2 has a large brightness deterioration at anentrance angle of 30°. Therefore, these two comparative examples areinferior in entrance angularity.

TABLE 1 Entrance Observa- Compara- angle tion angle Embodi- Embodi-Comparative tive (Degree) (Degree) ment 1 ment 2 example 1 example 2  50.2 1120  1080  820 780 0.33 612 580 430 390 10 0.2 910 830 580 515 0.33450 460 250 235 30 0.2 720 730 430 380 0.33 230 320  80  91

The present invention is a triangular-pyramidal cube-cornerretroreflective sheeting characterized in that triangular-pyramidalcube-corner retroreflective elements protruded beyond a common baseplane (X-X′) share a base edge (x) on the base plane and they are facedeach other and arranged on the base plane, the two facedtriangular-pyramidal reflective elements form an element pair faced eachother so as to be substantially symmetric to planes (Y-Y′, Y-Y′, . . . )vertical to the base plane including the shared base edge (x) on thebase plane and having the substantially same shape and thetriangular-pyramidal reflective elements are constituted of asubstantially-same hexagonal or triangular lateral face (face c) usingthe shared base edge (x) as one side and substantially-same quadrangularlateral faces (faces a and b) using two upper sides of the face cstarting with the apex (H of the triangular-pyramidal reflectiveelements as one sides and sharing one ridge line of thetriangular-pyramidal reflective elements and using the ridge line as oneside and substantially orthogonal to the face c₁ and when assuming theheight from the apex (h) of the triangular-pyramidal reflective elementsup to the base plane (X-X′) as (h), the height up to asubstantially-horizontal plane (Z-Z′) including base edges (z and w) oflateral faces (faces a and b) as (h₀), and the angle formed between theoptical axis of the triangular-pyramidal reflective elements and thevertical plane (Y-Y′) as (θ), h and h₀ are not substantially equal toeach other and h/h₀ and θ meet a specific relational expression.

Thereby, a retroreflective sheeting of the present invention makes itpossible to improve not only the high brightness characteristic, thatis, the level (magnitude) of the reflection brightness represented bythe reflection brightness of the light incoming from the front of thesheeting but also wide angularities such as observation angularity,entrance angularity, rotation angularity.

What is claimed is:
 1. A triangular-pyramidal cube-cornerretroreflective sheeting characterized in that triangular-pyramidalcube-corner retro-reflective elements protruded beyond a common baseplane (X-X′) are faced each other and arranged on the base plane (X-X′)in the closest-packed state by sharing one base edge on the base plane(X-X′), the base plane (X-X′) is a common plane including many baseedges (x, x, . . . ) shared by the triangular-pyramidal reflectiveelements, the two triangular-pyramidal reflective elements faced eachother constitute an element pair having substantially same shape facedso as to be respectively substantially symmetric to planes (Y-Y′, Y-Y′,. . . ) vertical to the base plane (X-X′) including many shared baseedges (x, x, . . . ) on the base plane (X-X′), the triangular-pyramidalreflective elements are constituted of substantially same hexagonal ortriangular lateral faces (prism faces) (faces c₁ and c₂) using theshared base edges (x, x, . . . ) as one sides and substantially samequadrangular lateral faces (faces a₁ and b₁ and faces a₂ and b₂)substantially orthogonal to the face c₁ or the face c₂ by using twoupper sides of the face c₁ or c₂ starting with apexes (H₁ and H₂) of thetriangular-pyramidal reflective elements as one sides and sharing oneridge line of the triangular-pyramidal reflective elements and using theridge line as one side, and when assuming the height from the apexes (H₁and H₂) of the triangular-pyramidal reflective elements up to the baseplane (X-X′) including the base edges (x, x, . . . ) of the hexagonal ortriangular lateral faces (faces c₁ and c₂) of the triangular-pyramidalreflective elements as (h), the height from the apexes (H₁ and H₂) ofthe triangular-pyramidal reflective elements up to a substantiallyhorizontal plane (Z-Z′) including base edges (z and w) of other lateralfaces (faces a₁ and b₁ and faces a₂ and b₂) of the triangular-pyramidalreflective elements as (h₀), the intersection between a vertical linefrom the apexes (H₁ and H₂) of the triangular-pyramidal reflectiveelements to the base plane (X-X′) and the base plane (X-X′) as P, theintersection between an optical axis passing through the apexes (H₁ andH₂) and the base plane (X-X′) as Q, and moreover, expressing distancesfrom the intersections (P) and (Q) up to planes (Y-Y′, Y-Y′, . . . )including the base edges (x, x, . . . ) shared by thetriangular-pyramidal reflective elements and vertical to the base plane(X-X′) as p and q, and assuming the angle formed between the opticalaxis and the vertical plane (Y-Y′) as (θ), the above h and h₀ are notsubstantially equal and meet the following expression (1)$\begin{matrix}{{0.5\quad R} \leqq \frac{h}{h_{0}} \leqq {1.5\quad R}} & (1)\end{matrix}$

(In the above expression, R has a value defined by the followingexpression.)$R = \frac{{\sin \left( {35.2644^{*} - \theta} \right)} + {1.2247\sin \quad \theta}}{\sin \left( {35.2644^{*} - \theta} \right)}$

(In the above expression, it is assumed that when the value of the above(p−q) is negative, θ takes a negative (−) value).
 2. Thetriangular-pyramidal cube-corner retroreflective sheeting according toclaim 1, characterized in that; when assuming the height from apexes (H₁and H₂) of triangular-pyramidal cube-corner retroreflective elements upto the base plane (X-X′) including base edges (x, x, . . . ) ofhexagonal or triangular lateral faces (faces c₁ and c₂) of thetriangular-pyramidal reflective elements as (h), the height up to asubstantially horizontal plane (Z-Z′) including base edges (z and w) ofother lateral faces (faces a₁ and b₁ and faces a₂ and b₂) of thetriangular-pyramidal reflective elements as (h₀), the intersectionbetween a vertical line extended from the apexes (H₁ and H₂) of thetriangular-pyramidal reflective elements up to the base plane (X-X′) andthe base plane (X-X′) as P, the intersection between an optical axispassing through the apexes (H₁ and H₂) and the base plane (X-X′) as Q,and moreover distances from the intersections (P) and (Q) up to planes(Y-Y′, Y-Y′, . . . ) including base edges (x, x, . . . ) shared by thetriangular-pyramidal reflective elements and vertical to the base plane(X-X′) as p and q, and the angle formed between the optical axis and thevertical plane (Y-Y′) as (θ), h and h₀ are not substantially equal toeach other but they meet the following expression (2) $\begin{matrix}{{0.6R}\quad \leqq \quad \frac{h}{h_{0}} \leqq \quad {1.4R}} & (2)\end{matrix}$

(In the above expression, R is the same as that defined in claim 1). 3.The triangular-pyramidal cube-corner retroreflective sheeting accordingto claim 1, characterized in that; when assuming the height from apexes(H₁ and H₂) of triangular-pyramidal cube-corner retroreflective elementsup to the base plane (X-X′) including base edges (x, x, . . . ) ofhexagonal or triangular lateral faces (faces c₁ and c₂) of thetriangular-pyramidal reflective elements as (h), the height up to asubstantially horizontal plane (Z-Z′) including base edges (z and w) ofother lateral faces (faces a₁ and b₁ and faces a₂ and b₂) of thetriangular-pyramidal reflective elements as (h₀), the intersectionbetween a vertical line extended from the apexes (H₁ and H₂) of thetriangular-pyramidal reflective elements up to the base plane (X-X′) andthe base plane (X-X′) as P, the intersection between an optical axispassing through the apexes (H₁ and H₂) and the base plane (X-X′) as Q,and moreover distances from the intersections (P) and (Q) up to planes(Y-Y′, Y-Y′, . . . ) including base edges (x, x, . . . ) shared by thetriangular-pyramidal reflective elements and vertical to the base plane(X-X′) as p and q, and the angle formed between the optical axis and thevertical plane (Y-Y′) as (θ), h and h₀ are not substantially equal toeach other but they meet the following expression (3) $\begin{matrix}{{0.8R}\quad \leqq \quad \frac{h}{h_{0}} \leqq \quad {1.2R}} & (3)\end{matrix}$

(In the above expression, R is the same as that defined in claim 1). 4.The triangular-pyramidal cube-corner retroreflective sheeting accordingto claim 1, characterized in that; among h, h₀, p, q, and θ definedabove, h and h₀ are not substantially equal to each other but they meetthe following expression (4) $\begin{matrix}{{0.85R}\quad \leqq \quad \frac{h}{h_{0}} \leqq \quad {1.15R}} & (4)\end{matrix}$

(In the above expression, R is the same as that defined in claim 1). 5.The triangular-pyramidal cube-corner retroreflective sheeting accordingto claim 1, characterized in that; when assuming the height from apexes(H₁ and H₂) of triangular-pyramidal cube-corner retroreflective elementsup to the base plane (X-X′) including base edges (x, x, . . . ) ofhexagonal or triangular lateral faces (faces c₁ and c₂) of thetriangular-pyramidal reflective elements as (h), the height up to asubstantially horizontal plane (Z-Z′) including base edges (z and w) ofother lateral faces (faces a₁ and b₁ and faces a₂ and b₂) of thetriangular-pyramidal reflective elements as (h₀), the intersectionbetween a vertical line extended from the apexes (H₁ and H₂) of thetriangular-pyramidal reflective elements up to the base plane (X-X′) andthe base plane (X-X′) as P, the intersection between an optical axispassing through the apexes (H₁ and H₂) and the base plane (X-X′) as Q,and moreover distances from the intersections (P) and (Q) up to planes(Y-Y′, Y-Y′, . . . ) including base edges (x, x, . . . ) shared by thetriangular-pyramidal reflective elements and vertical to the base plane(X-X′) as p and q, and the angle formed between the optical axis and thevertical plane (Y-Y′) as (θ), h and h₀ are not substantially equal toeach other but they meet the following expression (5) $\begin{matrix}{{0.3\left( {R - 1} \right)} \leqq \frac{h - h_{0}}{h_{0}} \leqq {1.5\left( {R - 1} \right)}} & (5)\end{matrix}$

(In the above expression, R is the same as that defined in claim 1). 6.The triangular-pyramidal cube-corner retroreflective sheeting accordingto claim 1, characterized in that; when assuming the height from apexes(H₁ and H₂) of triangular-pyramidal cube-corner retroreflective elementsup to the base plane (X-X′) including base edges (x, x, . . . ) ofhexagonal or triangular lateral faces (faces c₁ and c₂) of thetriangular-pyramidal reflective elements as (h), the height up to asubstantially horizontal plane (Z-Z′) including base edges (z and w) ofother lateral faces (faces a₁ and b₁ and faces a₂ and b₂) of thetriangular-pyramidal reflective elements as (h₀) the intersectionbetween a vertical line extended from the apexes (H₁ and H₂) of thetriangular-pyramidal reflective elements up to the base plane (X-X′) andthe base plane (X-X′) as P, the intersection between an optical axispassing through the apexes (H₁ and H₂) and the base plane (X-X′) as Q,and moreover distances from the intersections (P) and (Q) up to planes(Y-Y′, Y-Y′, . . . ) including base edges (x, x, . . . ) shared by thetriangular-pyramidal reflective elements and vertical to the base plane(X-X′) as p and q, and the angle formed between the optical axis and thevertical plane (Y-Y′) as (θ), h and h₀ are not substantially equal toeach other but they meet the following expression (6) $\begin{matrix}{{0.4\left( {R - 1} \right)} \leqq \frac{h - h_{0}}{h_{0}} \leqq {1.2\left( {R - 1} \right)}} & (6)\end{matrix}$

(In the above expression, R is the same as that defined in claim 1). 7.The triangular-pyramidal cube-corner retroreflective sheeting accordingto any one of claims 1 to 6, characterized in that the optical axis oftriangular-pyramidal cube-corner retroreflective elements tilts in thedirection in which the difference (q−p) between the distance (p) fromthe intersection (P) between a vertical line extended from apexes (H₁and H₂) of triangular-pyramidal cube-corner retroreflective elements toa base plane (X-X′) and the base plane (X-X′) up to the vertical plane(Y-Y′) including base edges (x, x, . . . ) shared by the element pairand the distance (q) from the intersection (Q) between the optical axisof the triangular-pyramidal reflective elements and the base plane(X-X′) up to the vertical plane (Y-Y′) becomes positive (+) or negative(−) and so as to form an angle of 3° to 15° from a vertical line (H₁-P)extended from apexes of the triangular-pyramidal reflective elements toa base plane (X-X′).
 8. The triangular-pyramidal cube-cornerretroreflective sheeting according to any one of claims 1 to 6,characterized in that the optical axis of triangular-pyramidalcube-corner retroreflective elements tilts in the direction in which thedifference (q−p) between the distance (p) from the intersection (P)between a vertical line extended from apexes (H₁ and H₂) oftriangular-pyramidal cube-corner retroreflective elements to a baseplane (X-X′) and the base plane (X-X′) up to the vertical plane (Y-Y′)including base edges (x, x, . . . ) shared by the element pair and thedistance (q) from the intersection (Q) between the optical axis of thetriangular-pyramidal reflective elements and the base plane (X-X′) up tothe vertical plane (Y-Y′) becomes positive (+) or negative (−) and so asto form an angle of 4° to 12° from a vertical line (H₁-P) extended fromapexes of the triangular-pyramidal reflective elements to a base plane(X-X′).
 9. The triangular-pyramidal cube-corner retroreflective sheetingaccording to any one of claims 1 to 6, characterized in that the opticalaxis of triangular-pyramidal cube-corner retroreflective elements tiltsin the direction in which the difference (q−p) between the distance (p)from the intersection (P) between a vertical line extended from apexes(H₁ and H₂) of triangular-pyramidal cube-corner retroreflective elementsto a base plane (X-X′) and the base plane (X-X′) up to the verticalplane (Y-Y′) including base edges (x, x, . . . ) shared by the elementpair and the distance (q) from the intersection (Q) between the opticalaxis of the triangular-pyramidal reflective elements and the base plane(X-X′) up to the vertical plane (Y-Y′) becomes positive (+) or negative(−) and so as to form an angle of 50° to 10° from a vertical line (H₁-P)extended from apexes of the triangular-pyramidal reflective elements toa base plane (X-X′).
 10. The triangular-pyramidal cube-cornerretroreflective sheeting according to claim 9, characterized in that thedistance (h₀) from a horizontal plane (Z-Z′) including base edges (z andw) of lateral faces (faces a₁ and b₁ or faces a₂ and b₂) formed by thefact that substantially-same-shape lateral faces (faces a₁ and b₁)sharing one ridge line starting with apexes (H₁ and H₂) oftriangular-pyramidal cube-corner retroreflective elements protrudedbeyond a common base plane (X-X′) and using the ridge line as one sideintersect with corresponding lateral faces (faces a₁ and b₁ or faces a₂and b₂) of their adjacent other triangular-pyramidal reflective elementsup to the apexes (H₁ and H₂) of the triangular-pyramidal reflectiveelements ranges between 40 and 250 μm.
 11. The triangular-pyramidalcube-corner retroreflective sheeting according to claim 9, characterizedin that the distance (h₀) from a horizontal plane (Z-Z′) including baseedges (z and w) of lateral faces (faces a₁ and b₁ or faces a₂ and b₂)formed by the fact that substantially-same-shape lateral faces (faces a₁and b₁) sharing one ridge line starting with apexes (H₁and H₂) oftriangular-pyramidal cube-corner retroreflective elements protrudedbeyond a common base plane (X-X′) and using the ridge line as one sideintersect with corresponding lateral faces (faces a₁ and b₁ or faces a₂and b₂) of their adjacent other triangular-pyramidal reflective elementsup to the apexes (H₁ and H₂) of the triangular-pyramidal reflectiveelements ranges between 50 and 200 μm.
 12. The triangular-pyramidalcube-corner retroreflective sheeting according to claim 10,characterized in that at least one prism face angle formed by the factthat three lateral faces (faces a₁, b₁, and c₁) or (faces a₂, b₂, andc₂) of a triangular-pyramidal cube-corner retroreflective elementintersect with each other ranges between 89.5° and 90.5°.
 13. Thetriangular-pyramidal cube-corner retroreflective sheeting according toclaim 10, characterized in that at least one prism face angle formed bythe fact that three lateral faces (faces a₁, b₁, and c₁) or (faces a₂,b₂, and c₂) of a triangular-pyramidal cube-corner retroreflectiveelement intersect with each other ranges between 89.7° and 90.3°. 14.The triangular-pyramidal cube-corner retroreflective sheeting accordingto claim 11, characterized in that at least one prism face angle formedby the fact that three lateral faces (faces a₁, b₁, and c₁) or (facesa₂, b₂ and c₂) of a triangular-pyramidal cube-corner retroreflectiveelement intersect with each other ranges between 89.5° and 90.5°. 15.The triangular-pyramidal cube-corner retroreflective sheeting accordingto claim 11, characterized in that at least one prism face angle formedby the fact that three lateral faces (faces a₁, b₁, and c₁) or (facesa₁, b₂ and c₂) of a triangular-pyramidal cube-corner retroreflectiveelement intersect with each other ranges between 89.7° and 90.3°.